Sinusoidal-Gaussian beams in complex optical systems

Abstract

Sinusoidal-Gaussian beam solutions are derived for the propagation of electromagnetic waves in free space and in media having at most quadratic transverse variations of the index of refraction and the gain or loss. The resulting expressions are also valid for propagation through other real and complex lens elements and systems that can be represented in terms of complex beam matrices. The solutions are in the form of sinusoidal functions of complex argument times a conventional Gaussian beam factor. In the limit of large Gaussian beam size, the sine and cosine factors of the beams are dominant and reduce to the conventional modes of a rectangular waveguide. In the opposite limit the beams reduce to the familiar fundamental Gaussian form. Alternate hyperbolic-sinusoidal-Gaussian beam solutions are also found.